Question

The hypotenuse of a Right Triangle is 2 m less than thrice the shortest side. The third side is 7 m more than the shortest side. Considering the shortest side as x cm, find all the sides of the right Triangle.

Answer 1

Step-by-step explanation:

Let the length of the shortest side be x meters.

Then, hypotenuse=(2x+6) metres

And the third side (2x+6−2) metre=(2x+4) metres

By Pythagoras theorem, we have

(2x+6)2=x2+(2x+4)2

⇒x2−8x−20=0

⇒x2−10x−2x−20=0

⇒(x−10)(x+2)=0

⇒x=10orx=−2

∵ x can not be a negative $$\therefore 

⇒x=10

Length of the shortest side =10 metres

Length of the hypotenuse =(2x+6) metres=26 metres

Length of the third side =(2x+4) metres=24 metres

Hence the sides of the triangle are 10m,26m and 24m